Yeah! It is possible to build an aircraft that flaps its wings to fly, but the fuel efficiency, complexity of design and cost required for that flight would be a burden to implement. This has been attempted in the past, but virtually all designs have failed, mostly for mechanical reasons.
The commercial aircraft and their working principles are a far more satisfactory design to carry payload in a cost-effective manner. An ornithopter design, were it successful, would require more energy and mechanical complexity to carry even a small payload.